Multiple choice

A rectangular field measures 100,000 ft by 100 ft. Ten regions are selected. The dimensions of each region are 1,000 ft by 100 ft and no two regions overlap. There are different number of plants planted in each region of the field. The number of plants planted in different regions are shown in the table below. Region Number of plants Region Number of plants 1 120 6 130 2 104 7 135 3 140 8 114 4 112 9 147 5 152 10 121 Which of the following is a reasonable approximation of the number of plants planted in the entire field?

  1. 1,280

  2. 12,800

  3. 128,000

  4. 1,280,000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The total area is 10,000,000 sq ft. Each region is 100,000 sq ft. There are 100 such regions in the field. The average number of plants per region is (120+104+140+112+152+130+135+114+147+121)/10 = 1275/10 = 127.5. Total plants = 127.5 * 100 = 12,750. The closest approximation is 12,800.

AI explanation

First, calculate the average number of plants per selected region by dividing the total number of plants in the ten sampled regions by ten, which is 1280 / 10 = 128 plants. Since the total area of the field is 100000 ft x 100 ft = 10000000 sq ft and the area of one region is 1000 ft x 100 ft = 100000 sq ft, there are exactly 100 such non-overlapping regions in the entire field. Multiplying the 100 regions by the average of 128 plants gives an approximation of 12800 plants for the whole field.

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